群体智能与仿生计算：最新优化算法详解

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《群体智能与生物启发计算：概述》是一本由Xin-She Yang和Mehmet Karamanoglu合著的经典电子书，两位作者来自英国 Middlesex University 的设计工程与数学学院，科学与技术学校。这本书在过去的二十年间广受关注，主要因为群体智能（Swarm Intelligence，简称SI）和生物启发计算在众多领域的广泛应用和显著优势。群体智能作为一种模仿自然界中蜜蜂、蚂蚁等生物群体行为的计算方法，其灵活性和适应性使其在优化问题上大放异彩。这些算法能够处理非线性设计问题，并且在现实世界中找到了广泛的应用，如数据挖掘、优化技术、人工智能决策、商业规划，甚至生物信息学和工业应用。它们的特点在于其高度并行处理能力，以及对复杂系统中涌现智慧的模拟。从优化的角度来看，群体智能的研究不仅限于数学模型，而是跨越了多学科边界，涉及到统计学、计算机科学、机器学习、经济学等多个领域。通过模拟蜜蜂的社会组织结构、蚂蚁的协作觅食策略、鸟类的群体导航等自然现象，研究人员得以开发出高效解决实际问题的新方法，如粒子群优化（Particle Swarm Optimization, PSO）、蚁群优化（Ant Colony Optimization, ACO）和遗传算法（Genetic Algorithm, GA）等。书中详细探讨了这些算法的工作原理、进化过程、优缺点以及如何在特定场景中优化使用。此外，它还涵盖了如何将生物界的行为原则应用于设计复杂的系统，如机器人协作、物流优化、网络路由等问题。生物启发计算的发展也推动了跨学科研究的深入，促进了理论与实践的紧密结合。《群体智能与生物启发计算：概述》不仅提供了一个深入理解这一领域基础知识的平台，还为读者揭示了如何将这种强大的计算工具应用于解决现代世界的复杂挑战，是IT专业人员和跨学科研究者不可或缺的参考资料。

As a further approximation, this last assumption can be approximated by a frac-

tion p

of the n host nests which are replaced by new nests (with new random solu-

tions). For a maximization problem, the quality or fitness of a solution can simply

be proportional to the value of the objective function. Other forms of fitness can be

defined in a similar manner to the fitness function in genetic algorithms.

From the implementation point of view, we can use the following simple repre-

sentations: each egg in a nest represents a solution, and each cuckoo can lay only

one egg (thus representing one solution); the aim is to use the new and potentially

better solutions (cuckoos) to replace a not-so-good solution in the nests. Obviously,

this algorithm can be extended to a more complicated case where each nest has

multiple eggs representing a set of solutions. For this present introduction, we use

the simplest approach where each nest has only a single egg. In this case, there is

no distinction between egg, nest, or cuckoo, as each nest corresponds to one egg

which also represents one cuckoo.

This algorithm uses a balanced combination of a local random walk and the

global explorative random walk, controlled by a switching parameter p

. The local

random walk can be written as

t11

5 x

1 αs  Hðp

2 εÞðx

2 x

Þð1:20Þ

where x

and x

are two different solutions selected randomly by random permuta-

tion, HðuÞ is a Heaviside function, ε is a random number drawn from a uniform dis-

tribution, and s is the step size. On the other hand, the global random walk is

carried out by using Le

vy flights

t11

5 x

1 αLðs; λÞð1:21Þ

where

Lðs; λÞ 5

λΓðλÞ sin ðπλ=2Þ

11λ

; ðscs

. 0Þð1:22Þ

Here α . 0 is the step-size-scaling factor, which should be related to the scales

of the problem of interests. In most cases, we can use α 5 OðL=10Þ, where L is the

characteristic scale of the problem of interest, while in some cases α 5 OðL=100Þ

can be more effective and can avoid flying too far. Equation (1.22) is essentially

the stochastic equation for a random walk. In general, a random walk is a Markov

chain whose next status/location only depends on the current location (the first

term in Eq. (1.22)) and the transition probability (the second term). However, a

substantial fraction of the new solutions should be generated by far field randomi-

zation and whose locations should be far enough from the current best solution.

This will make sure that the system does not get trapped in a local optimum (

Yang

and Deb, 2010

18 Swarm Intelligence and Bio-Inspired Computation

A Matlab implementation is given by the author and can be downloaded.

Cuckoo search is very efficient in solving engineering optimization problems

(

Gandomi et al., 2013; Yang and Deb, 2009).

1.5.7 Flower Pollination Algorithm

Flower pollination algorithm (FPA) was developed by Yang (2012) inspired by the

flow pollin ation process of flowering plants:

1. Biotic and cross-pollination can be considered as a process of global pollination process,

and pollen-carrying pollinators move in a way that obeys Le

vy flights (Rule 1).

2. For local pollination, abiotic and self-pollination are used (Rule 2).

3. Pollinators such as insects can develop flower constancy, which is equivalent to a repro-

duction probability that is proportional to the similarity of two flowers involved (Rule 3).

4. The interaction or switching of local pollination and global pollination can be controlled

by a switch probability pA½0; 1, with a slight bias toward local pollination (Rule 4).

In order to formulate updating formulas, we have to convert the aforementioned

rules into updating equations. For example, in the global pollination step, flower

pollen gametes are carried by pollinators such as insects, and pollen can travel over

a long distance because insects can often fly and move in a much longer range.

Therefore, Rule 1 and flower constancy can be represented mathematically as

t11

5 x

1 LðλÞðx

2 g



Þð1:23Þ

where x

is the pollen i or solution vector x

at iteration t, and g



is the current best

solution found among all solutions at the current generation/iteration. Here LðλÞ is

the parameter that corresponds to the strength of the pollination, which essentially

is also a step size. Since insects may move over a long distance with various dis-

tance steps, we can use a Le

vy flight to mimic this characteristic efficiently. That

is, we draw L . 0 from a Le

vy distribution as described in

Eq. (1.22).

For the local pollin ation, both Rule 2 and Rule 3 can be represented as

t11

5 x

1 εðx

2 x

Þð1:24Þ

where x

and x

are pollen from different flowers of the same plant species. This essen-

tially mimics the flower constancy in a limited neighborhood. Mathematically, if x

and x

come from the same species or selected from the same population, this equiva-

lently becomes a local random walk if we draw ε from a uniform distribution in [0,1].

In principle, flower pollination activities can occur at all scales, both local and

global. But in reality, adjacent flower patches or flowers in the not-so-far-away

neighborhood are more likely to be pollinated by local flowe r pollen than those far

away. In order to mimic this feature, we can effectively use a switch probability

(Rule 4) or proximity probability p to switch between common global pollination

www.mathworks.com/matlabcentral/fileexchange/29809-cuckoo-search-cs-algorithm.

19Swarm Intelligence and Bio-Inspired Computation: An Overview

and intensive local pollination. To start with, we can use a naive value of p 5 0:5

as an initial value. A preliminary parametric showed that p 5 0:8 may work better

for most applications (

Yang, 2012).

1.5.8 Other Algorithms

There are many other metahe uristic algorithms, which may be equally popular

and powerful, and these include Tabu search (

Glover and Laguna, 1997), artificial

immune system (

Farmer et al., 1986), and others (Koziel and Yang, 2011; Wolpert

and Macready, 1997; Yang, 2010a, b). For example, wolf search algorithm (WSA)

was developed recently by Rui et al. (2012)

based on the wolf pack predating

behavior. Preliminary results show that WSA is a very promising algorithm with

convincing performance. Other algorithms such as Krill herd algorithm and artifi-

cial plant algorithm are described in detail in some relevant chapters of this book.

The efficiency of metaheuristic algorithms can be attributed to the fact that they

try to imitate the best features in nature, especially the selection of the fittest in bio-

logical systems, which have evolved by natural selection over millions of years.

1.6 Open Problems and Further Research Topics

We have seen that SI and bio-inspired computing have demonstrated a great success

in solving various tough optimization problems, and there are still some challenging

issues, some of whi ch have been discussed in

Section 1.2. In order to inspire further

search in this area, we now summarize some of the key open problems:

Theoretical analysis of algorithm convergence: Up to now, only a small fraction of meta-

heuristic algorithms has some limited mathematical analyses in terms of convergence.

More studies are necessary to gain insight into various new algorithms. It is also highly

needed to build a framework for theoretical algorithm analysis.

Classification and terminology: There is still some confusion in terms of classifications

and terminologies used in the current literature. Further studies should also try to classify

all known algorithms by some agreed criteria and ideally also to unify the use of key ter-

minologies. This requires the effort by all researchers in the wider communities to partici-

pate and to dedicate their usage in future publications.

Parameter tuning: The efficiency of an algorithm may depend on its algorithm-dependent

parameters, and optimal parameter setting of any algorithm itself is an optimization prob-

lem. To find the best methods to tune these parameters are still under active research.

It can be expected that algorithms with automatic parameter tuning will be a good para-

digm shift in the near future.

Large-scale problems: Most current studies in bio-inspired computing have focused on

the toy problems and small-scale problems. For large-scale problems, it still remains

untested if the same methodology for solving toy problems can be used to get solutions

efficiently. For linear programming, it was basically the case; however, nonlinearity often

poses greater challenges.

Truly intelligent algorithms: Researchers have strived to develop better and smarter algo-

rithms for many years, but truly intelligent algorithms are yet to emerge. This could be

the holy grail of optimization and computational intelligence.

20 Swarm Intelligence and Bio-Inspired Computation

Obviously, challenges also bring opportunities. There is no exaggeration to say

that it is a golden time for bio-inspired computing so that researchers can rethink

existing methodologies and approaches more deeply and perhaps differently. It is

possible that significant progress can be made in the next 10 years. Any progress in

theory and in large-scale practice will provide great insight and may ultimately

alter the research landscape in metaheuristics. It is can be expected that som e truly

intelligent, self-evolving algorithms may appear to solve a wide range of tough

optimization and classification problems efficiently in the not-so-far future.

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群体智能与仿生计算：最新优化算法详解

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